## Calculator 2 years ago EXPAND sqrt{/frac{1-x}{1+x}}

1. Calculator

$\Huge \sqrt{\frac{1-x}{1+x}}$

2. Calculator

up to power x^2

3. Calculator

i get $1-x+\frac{x^2}{2} - \frac{x^3}{8} - \frac{3x^4}{64}$

4. Calculator

@saifoo.khan

5. Calculator

wolfram got $-\frac{3 x^5}{8}+\frac{3 x^4}{8}-\frac{x^3}{2}+\frac{x^2}{2}-x+1$

6. saifoo.khan

Unfortunately i forgot the formula! D:

7. wio

Is it a maclaurin series?

8. Calculator

you can try that

9. wio

I want to know what is meant by Expand, since that's the only thing that comes to mind.

10. Calculator

you can use this $(x+a)^n=\sum ^{n}_{ k=0} \left(\begin{matrix}n \\ k\end{matrix}\right) x^k a^{(n-k)}$

11. Calculator

or $(1+x)^n = 1+nx+\frac{(n)(n-1)}{2!}(x^2)+...$

12. wio

That works for $$n\in \mathbb{N}$$.

13. wio

In this case you have a square root...

14. Calculator

still can, watch

15. Calculator

$\sqrt{\frac{1-x}{1+x}} \\ \\ \frac{\sqrt{1-x}}{\sqrt{1+x}} \\ \\ (1-x)^\frac{1}{2}(1+x)^{-\frac{1}{2}}$

16. Calculator

expand separately

17. Calculator

mix them by multiplying together

18. wio

Yeah, my problem is with $$1/2 \notin \mathbb{N}$$

19. Calculator

I don't think it should be natural number

20. Calculator

i mean real number will do

21. wio

How can you have summations or binomial coefficients with rational numbers?

22. amoodarya

interval of x is ?

23. Calculator

the formula list says can use

24. Calculator

we use the second one (1+x)^n

25. Calculator

http://en.wikipedia.org/wiki/Binomial_series look at the History section

26. amoodarya

|dw:1359798673882:dw|

27. amoodarya

|dw:1359798819059:dw|

28. Calculator

or maybe its $-\frac{3 x^5}{8}+\frac{3 x^4}{8}-\frac{x^3}{2}+\frac{x^2}{2}-x+1$

29. Calculator

hmm

30. Calculator

based from the formula as long as its in the from ("1"+x)^n should be fine to expand, i tried it

31. Calculator

from $(1-x)^{1/2} \\ \\ n=-1/2, x=-x(for formula) \\ \\ [1-\frac{x}{2}+\frac{(\frac{1}{2})(\frac{1}{2}-1)}{2}(x^2)] \\ \\ 1-\frac{x}{2}-\frac{x^2}{8}$